Finite Group Databasebeta

← #414984

Subgroups — #414984

Order 512.

1990 conjugacy classes of subgroups.

The subgroup lattice has 901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#121C211yesmaximal, characteristic
2C2×#1948C211yesmaximal, characteristic, complemented
3C2×#1802C211yesmaximal, characteristic, complemented
4C2×#1802C211yesmaximal, characteristic, complemented
5C2×#1797C211yesmaximal, characteristic, complemented
6#14686C211yesmaximal, characteristic, complemented
7#11293C212yesmaximal, complemented
8#11121C212yesmaximal, complemented
9#11095C212yesmaximal, complemented
10#10969C212yesmaximal
11#10849C211yesmaximal, characteristic, complemented
12C22×#121C2211yescharacteristic
13C22×C4×D4—21no—
14C22×C4×D4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C22×#106C2212yes—
17C22×C4⋊C8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×#102C2212yes—
20C22×#102C2212yes—
21C22×C22⋊C8C2212yes—
22C4×#121—24no—
23C4×#121—24no—
24C2×#390C2211yescharacteristic
25C2×#389C2211yescharacteristic
26C2×#388—21no—
27C2×#386—21no—
28C2×#384C2211yescharacteristic
29C2×#384C2211yescharacteristic
30C2×#380—21no—
31C2×#380—21no—
32C2×#380C2211yescharacteristic
33C2×#380C2212yes—
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4—21no—
36#1948—24no—
37#1802—24no—
38#1802—24no—
39#1797—24no—
40C2×#340C2212yes—
41C2×#340C2212yes—
42C2×#340C2212yes—
43C2×#340C2212yes—
44C2×#340C2212yes—
45C2×#336C2212yes—
46C4⋊#95—21no—
47C4⋊#95—21no—
48C4⋊#95C2212yes—
49C23×D4—21no—
50C23×D4C2311yescharacteristic
51C24×C4—21no—
52C24×C4D411yescharacteristic
53C24×C4D411yescharacteristic
54C24×C4C2311yescharacteristic
55C23×C8C2312yes—
56C23×C8C2312yes—
57C2×#121—22no—
58C2×#121—22no—
59C2×#121—22no—
60C2×#121—22no—
61C2×#121—22no—
62C2×#121Q814yes—
63C2×C4×D4—28no—
64C2×C4×D4—22no—
65C2×C4×D4—22no—
66C2×C4×D4—22no—
67C2×C4×D4—22no—
68C2×C4×D4—22no—
69C2×C4×D4—44no—
70C2×C4×D4—44no—
71C2×C4×D4D414yes—
72C22×C4⋊C4—21no—
73C22×C4⋊C4—21no—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4C2312yes—
78C22×C4⋊C4C2312yes—
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C22⋊C4—21no—
83C22×C22⋊C4—21no—
84C22×C22⋊C4—21no—
85C22×C22⋊C4—21no—
86C22×C22⋊C4—21no—
87C22×C22⋊C4—22no—
88C22×C42—21no—
89C22×C42—22no—
90C22×C42—22no—
91C22×C42—22no—
92C22×C42—22no—
93C22×C42—22no—
94C22×C42—22no—
95C22×C42D411yescharacteristic
96C22×C42D411yescharacteristic
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C2×#106—24no—
100C2×#106—42no—
101C2×#106—42no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—22no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8D414yescomplemented
108C2×#102—24no—
109C2×#102—24no—
110C2×#102—24no—
111C2×#102—42no—
112C2×#102—42no—
113C2×#102—42no—
114C2×C22⋊C8—24no—
115C2×C22⋊C8—24no—
116C2×C22⋊C8—42no—
117#390—22no—
118#390—22no—
119#389—22no—
120#389—22no—
121#388—28no—
122#386—28no—
123#384—22no—
124#384—22no—
125#384—22no—
126#384—22no—
127#380—22no—
128#380—22no—
129#380—42no—
130#380—42no—
131#380—44no—
132#380—44no—
133C4×C4⋊C4—22no—
134C4×C4⋊C4D414yes—
135C4×C22⋊C4—28no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—22no—
140C2×#95—22no—
141C2×#95—22no—
142#340—24no—
143#340—24no—
144#340—24no—
145#340—24no—
146#340—42no—
147#336—24no—
148C25—21no—
149C25C2×D411yescharacteristic
150C22×D4—24no—
151C22×D4—24no—
152C22×D4—24no—
153C22×D4—21no—
154C22×D4—21no—
155C22×D4—21no—
156C22×D4—21no—
157C22×D4—21no—
158C22×D4—21no—
159C22×D4—21no—
160C22×D4—21no—
161C22×D4—21no—
162C22×D4—21no—
163C22×D4—21no—
164C22×D4—42no—
165C22×D4—42no—
166C22×D4—42no—
167C22×D4—42no—
168C22×D4C2×D412yes—
169C22×D4C2×Q812yes—
170C22×D4#4112yes—
171C23×C4—22no—
172C23×C4—21no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—24no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—41no—
201C23×C4—41no—
202C23×C4—42no—
203C23×C4—42no—
204C23×C4—42no—
205C23×C4—42no—
206C23×C4—42no—
207C23×C4—42no—
208C23×C4SD1614yes—
209C23×C4C2×D411yescharacteristic
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×Q812yes—
215C23×C4#4112yes—
216C23×C4C2411yescharacteristic
217C22×C8—22no—
218C22×C8—22no—
219C22×C8—22no—
220C22×C8—22no—
221C22×C8—22no—
222C22×C8—22no—
223C22×C8—22no—
224C22×C8—22no—
225C22×C8—22no—
226C22×C8—22no—
227C22×C8—22no—
228C22×C8—22no—
229C22×C8—22no—
230C22×C8C2×D414yes—
231#121—28no—
232#121—28no—
233#121—28no—
234#121—28no—
235C4×D4—28no—
236C4×D4—28no—
237C4×D4—432no—
238C4×D4—44no—
239C4×D4—44no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4C2×D412yes—
281C2×C4⋊C4C2×D412yes—
282C2×C4⋊C4C2×D412yes—
283C2×C4⋊C4C2×Q812yes—
284C2×C4⋊C4#4112yes—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—42no—
297C2×C22⋊C4—42no—
298C2×C22⋊C4—42no—
299C2×C22⋊C4—42no—
300C2×C22⋊C4—44no—
301C2×C22⋊C4—44no—
302C2×C22⋊C4—44no—
303C2×C42—24no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—42no—
317C2×C42—42no—
318C2×C42—44no—
319C2×C42—44no—
320C2×C42—44no—
321C2×C42—44no—
322C2×C42C2×D412yes—
323C2×C42C2×D412yes—
324C2×C42C2×D412yes—
325C2×C42#4112yes—
326C2×C42#4112yes—
327C2×C42#4112yes—
328#106—48no—
329C4⋊C8—28no—
330C4⋊C8—44no—
331#102—48no—
332#102—48no—
333C22⋊C8—48no—
334#95—24no—
335#95—24no—
336#95—24no—
337#95—44no—
338#95—44no—
339#95—44no—
340C24—21no—
341C24—21no—
342C24—21no—
343C24—21no—
344C24—21no—
345C24—21no—
346C24—21no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—22no—
353C24—22no—
354C24—22no—
355C24—41no—
356C24—41no—
357C24—41no—
358C24—41no—
359C24—41no—
360C24—41no—
361C24—41no—
362C24—41no—
363C24—41no—
364C24—41no—
365C24—41no—
366C24—41no—
367C24C22⋊Q812yes—
368C24C2×SD1612yes—
369C24AGL(1,ℤ/8)12yes—
370C24C22×D411yescharacteristic
371C2×D4—216no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—48no—
388C2×D4—48no—
389C2×D4—48no—
390C2×D4—48no—
391C2×D4—48no—
392C2×D4—48no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4C22⋊Q814yes—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—28no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—28no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—44no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—44no—
475C22×C4—44no—
476C22×C4—44no—
477C22×C4—44no—
478C22×C4—44no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—84no—
509C22×C4—84no—
510C22×C4—84no—
511C22×C4—84no—
512C22×C4#12012yes—
513C22×C4#12012yes—
514C22×C4#12112yes—
515C22×C4#12112yes—
516C22×C4C22⋊Q812yes—
517C22×C4#12312yes—
518C22×C4#12312yes—
519C22×C4C2×SD1612yes—
520C22×C4C2×SD1612yes—
521C22×C4#13512yes—
522C22×C4AGL(1,ℤ/8)12yes—
523C22×C4AGL(1,ℤ/8)12yes—
524C22×C4#13712yes—
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×Q811yescharacteristic
529C22×C4C2×#4111yescharacteristic
530C22×C4C2×#4111yescharacteristic
531C22×C4C2×#4111yescharacteristic
532C22×C4C2×#4111yescharacteristic
533C22×C4C2×#4111yescharacteristic
534C22×C4C2×#4111yescharacteristic
535C22×C4H(5,𝔽2)11yescharacteristic
536C22×C4H(5,𝔽2)11yescharacteristic
537C22×C4H(5,𝔽2)11yescharacteristic
538C22×C42−1+411yescharacteristic
539C2×C8—24no—
540C2×C8—24no—
541C2×C8—24no—
542C2×C8—42no—
543C2×C8—42no—
544C2×C8—42no—
545C2×C8—42no—
546C2×C8—42no—
547C2×C8—42no—
548C2×C8—42no—
549C2×C8—42no—
550C2×C8—42no—
551C2×C8—42no—
552C2×C8—42no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—48no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—84no—
574C4⋊C4—84no—
575C4⋊C4—84no—
576C4⋊C4—84no—
577C4⋊C4C22⋊Q814yes—
578C22⋊C4—216no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—88no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—44no—
589C42—44no—
590C42—48no—
591C42#12114yes—
592C42#12114yes—
593C42#12314yes—
594C42#12414yes—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—81no—
649C23—81no—
650C23—81no—
651C23—81no—
652C23—81no—
653C23—81no—
654C23—81no—
655C23—81no—
656C23—81no—
657C23—81no—
658C23—81no—
659C23—81no—
660C23—81no—
661C23—81no—
662C23—81no—
663C23—81no—
664C23#47614yes—
665C23C2×#12011yescharacteristic
666C23C2×#12111yescharacteristic
667C23C2×C22⋊Q811yescharacteristic
668C23C2×#12311yescharacteristic
669C23#52511yescharacteristic
670C23#53511yescharacteristic
671C23#53711yescharacteristic
672C23C22×SD1611yescharacteristic
673C23C2×#13511yescharacteristic
674C23C2×AGL(1,ℤ/8)11yescharacteristic
675C23C2×AGL(1,ℤ/8)11yescharacteristic
676C23C2×AGL(1,ℤ/8)11yescharacteristic
677C23C2×#13711yescharacteristic
678C23#57511yescharacteristic
679C23#57511yescharacteristic
680D4—24no—
681D4—24no—
682D4—432no—
683D4—42no—
684D4—42no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—416no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—416no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—816no—
748C2×C4—82no—
749C2×C4—82no—
750C2×C4—82no—
751C2×C4—82no—
752C2×C4—82no—
753C2×C4—82no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4—82no—
759C2×C4—82no—
760C2×C4—82no—
761C2×C4—82no—
762C2×C4#39414yes—
763C2×C4#39414yes—
764C2×C4#44914yes—
765C2×C4#45014yes—
766C2×C4#46514yes—
767C2×C4#46914yes—
768C2×C4#48114yes—
769C2×C4#48214yes—
770C2×C4C2×#12111yescharacteristic
771C2×C4C2×#12111yescharacteristic
772C2×C4C2×C22⋊Q811yescharacteristic
773C2×C4C2×C22⋊Q811yescharacteristic
774C2×C4C2×#12311yescharacteristic
775C2×C4#52511yescharacteristic
776C2×C4#52511yescharacteristic
777C2×C4C2×#12411yescharacteristic
778C2×C4#53511yescharacteristic
779C2×C4#53511yescharacteristic
780C2×C4#53711yescharacteristic
781C2×C4#53711yescharacteristic
782C2×C4#54611yescharacteristic
783C2×C4#54611yescharacteristic
784C2×C4D4×Q811yescharacteristic
785C2×C4#55011yescharacteristic
786C2×C4#55211yescharacteristic
787C2×C4#55211yescharacteristic
788C2×C4#55311yescharacteristic
789C2×C4#55311yescharacteristic
790C2×C4#55311yescharacteristic
791C2×C4#55311yescharacteristic
792C2×C4#55411yescharacteristic
793C2×C4#55411yescharacteristic
794C2×C4#55411yescharacteristic
795C2×C4#55511yescharacteristic
796C2×C4#55511yescharacteristic
797C2×C4#55611yescharacteristic
798C8—44no—
799C8—82no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22C2×#39411yescharacteristic
831C22#241411yescharacteristic
832C22#241711yescharacteristic
833C22#248511yescharacteristic
834C22#248711yescharacteristic
835C22#261511yescharacteristic
836C22#284811yescharacteristic
837C22C2×#45011yescharacteristic
838C22C2×#44911yescharacteristic
839C22#300611yescharacteristic
840C22#300711yescharacteristic
841C22C2×#46511yescharacteristic
842C22C2×#46911yescharacteristic
843C22#305511yescharacteristic
844C22#305611yescharacteristic
845C22C2×#47611yescharacteristic
846C22#307611yescharacteristic
847C22#307711yescharacteristic
848C22#307911yescharacteristic
849C22C2×#48211yescharacteristic
850C22C2×#48111yescharacteristic
851C22#309211yescharacteristic
852C22#309311yescharacteristic
853C22#310111yescharacteristic
854C22#310711yescharacteristic
855C22#310911yescharacteristic
856C22#311511yescharacteristic
857C22#320611yescharacteristic
858C22#321211yescharacteristic
859C22#321411yescharacteristic
860C22#321711yescharacteristic
861C22#324611yescharacteristic
862C22#324711yescharacteristic
863C22#325111yescharacteristic
864C22#325411yescharacteristic
865C4—24no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—44no—
870C4—82no—
871C4—82no—
872C4—162no—
873C4—162no—
874C4#203418yes—
875C4#241411yescharacteristic
876C4#241711yescharacteristic
877C4#248511yescharacteristic
878C4#248711yescharacteristic
879C4#253511yescharacteristic
880C4#253811yescharacteristic
881C4#256211yescharacteristic
882C4#256311yescharacteristic
883C2—44no—
884C2—84no—
885C2#1518111yescharacteristic
886C2C2×#203411yescharacteristic
887C2#2348211yescharacteristic
888C2#2465111yescharacteristic
889C2#2465811yescharacteristic
890C2#2483611yescharacteristic
891C2#2484411yescharacteristic
892C2#2762511yescharacteristic
893C2#2762711yescharacteristic
894C2#2767811yescharacteristic
895C2#2767911yescharacteristic
896C2#2966211yescharacteristic
897C2#2966311yescharacteristic
898C2#3295511yescharacteristic
899C2#3295611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#1948C2semidirect
3. C2×#1802C2semidirect
4. C2×#1802C2semidirect
5. C2×#1797C2semidirect
6. #14686C2semidirect
7. #11293C2semidirect
8. #11121C2semidirect
9. #11095C2semidirect
11. #10849C2semidirect
107. C2×C4⋊C8D4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×#1212
C2×#19482
C2×#18022
C2×#17972
#146862
#112932
#111212
#110952
#109692
#108492